In the Acts of the Apostles, there's a relevant passage about converting the Gentiles (non-Jewish people). James has this to say:
It is my judgment, therefore, that we ought to stop troubling the Gentiles who turn to God, but tell them by letter to avoid pollution from idols, unlawful marriage, the meat of strangled animals, and blood.All of the legalisms of Judaism are replaced by a few, simple rules* so that the Church can concentrate on what's important. Had they not done this, they would have first had to convert the Gentiles to Judaism and then from there to Christianity. Judaism would have been the undergraduate degree and Christianity the graduate degree. Clearly, that's not what they did, that's not what we do and not what we preach.
Ergo, the Old Testament verses flung thither and yon are not the snares some make them out to be.
* - We don't worry so much about strangled animals or blood any more.